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Abstract

A common assumption used in statistical signal processing of nonstationary random signals is that the signals are locally stationary. Using this assumption, data is segmented into short analysis frames, and processing is performed using these short frames. Short frames limit the amount of data available, which in turn limits the performance of statistical estimators. In this thesis, we propose a novel method that promises improved performance for a variety of statistical signal processing algorithms. This method proposes to estimate certain time-varying parameters of nonstationary signals and then use this estimated information to perform a time-warping of the data that compensates for the time-varying parameters. Since the time-warped data is more stationary, longer analysis frames may be used, which improves the performance of statistical estimators. We first examine the spectral statistics of two particular types of nonstationary random processes that are useful for modeling ship propeller noise and voiced speech. We examine the effect of time-varying frequency content on these spectral statistics, and in addition show that the cross-frequency spectral statistics of these signals contain significant additional information that is not usually exploited using a stationary assumption. This information, combined with our proposed method, promises improvements for a wide variety of applications in the future. We then describe and test an implementation of our time-warping method, the fan-chirp transform. We apply our method to two applications, detection of ship noise in a passive sonar application and joint denoising and dereverberation of speech. Our method yields improved results for both applications compared to conventional methods.